Mathematics

Mathematics

Problem

Let

\mathbf a=(k,2,3)

and

\mathbf b=(1,k,4)

, where

k\in\mathbb R

. (i) Find all values of

k

for which

\mathbf a

and

\mathbf b

are perpendicular. (ii) For each value of

k

obtained in part (i), calculate

|\mathbf a|

and

|\mathbf b|

. (iii) For the same value(s) of

k

, verify that

|\mathbf a-\mathbf b|^{2}=|\mathbf a|^{2}+|\mathbf b|^{2}

.

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